You need to adjust your strategy depending on the amount of wind.

If there is little wind, a long straight coast is very satisfying. Just
a touch of reverse at the mooring will stop you right at the pin.

If there is substantial wind, you need a faster approach to keep
steerage so as not to be blown to the side at the last moment. Approach
quickly enough that you need to give a good strong hit of reverse just
before you go forward.

As Roger says, before leaving the helm make sure you are truly stopped.
Most mooring misses are because the boat is still moving while you are
getting forward. Also, if you are not happy with the situation don't
leave the helm but make an early decision to go around again.

Back in the grand days of racing schooners, I'm told there was a 130'
engineless beauty whose captain would enter Marblehead harbor under
full sail - wing and wing with all jibs flying. Just before hitting the
yacht club porch with his bowsprit, he would put down the helm turning
180 degrees to shoot his mooring. She could coast close to a 1/2 mile
into the wind before coming to rest. This gave the crew time to drop
and furl the sails and even put on the sail covers. As the huge
schooner came to a perfect stop, the steward would be serving drinks
to the owner's party as a single crewman reached down with a boat hook
to pick up a limp mooring pennant. With no engine and the sails under
cover there was no room for error.

Carl